Geometric reconstructions of density based clusterings

TL;DR

This paper introduces a geometric approach to reconstruct density-based clusters like DBSCAN* and HDBSCAN* from specific subsets of large datasets, enabling their application to very large data in real-world scenarios.

Contribution

It provides a systematic method to construct density-based clusters from manageable subsets, overcoming computational limitations for large datasets.

Findings

Theoretical proof of reconstructing clusters from subsets.

Application to large-scale Microsoft Building Footprint data.

Demonstration of clustering feasibility on big datasets.

Abstract

DBSCAN* and HDBSCAN* are well established density based clustering algorithms. However, obtaining the clusters of very large datasets is infeasible, limiting their use in real world applications. By exploiting the geometry of Euclidean space, we prove that it is possible to systematically construct the DBSCAN* and HDBSCAN* clusters of a finite $X\subset \mathbb{R}^n$ from specific subsets of $X$. We are able to control the size of these subsets and therefore our results make it possible to cluster very large datasets. To illustrate our theory, we cluster the Microsoft Building Footprint Database of the US, which is not possible using the standard implementations.